A163858 Number of sexy prime triples (p, p+6, p+12) where p+18 is not prime (although p-6 might be), with p <= n.

0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 6, 6, 6, 6, 7, 7, 7, 7, 7

Offset

1,17

Comments

p-6 will be prime if the prime triple contains the last 3 primes of a sexy prime quadruple.

There are two sexy prime triples classes, (-1, -1, -1) (mod 6) and (+1, +1, +1) (mod 6). They should asymptotically have the same number of triples, if there is an infinity of such triples, although with a Chebyshev bias expected against the quadratic residue class triples (+1, +1, +1) (mod 6), which doesn't affect the asymptotic result. This sequence counts both classes.

Also the sexy prime triples of class (-1, -1, -1) (mod 6) fall within (11, 17, 23, 29) (mod 30) while the sexy prime triples of class (+1, +1, +1) (mod 6) fall within (1, 7, 13, 19) (mod 30).

Links

Daniel Forgues, Table of n, a(n) for n=1..99982

Crossrefs

A046118 Smallest member of a sexy prime triple: value of p where (p, p+6, p+12) are all prime but p+18 is not (although p-6 might be.)

A046119 Middle member of a sexy prime triple: value of p+6 where (p, p+6, p+12) are all prime but p+18 is not (although p-6 might be.)

A046120 Largest member of a sexy prime triple, value of p+12 where (p, p+6, p+12) are all prime but p+18 is not (although p-6 might be.)

Sequence in context: A258198 A204562 A135660 * A236362 A133502 A341422

Adjacent sequences: A163855 A163856 A163857 * A163859 A163860 A163861

Keyword

nonn

Author

Daniel Forgues, Aug 05 2009, Aug 12 2009

Status

approved